As you guys know, Neil Paine is theman. Here’s the latest reason: he came up with a metric called True Receiving Yards, the latest in a long line of thoughts in our Wide Receiver Project. So, what are True Receiving Yards?

3) Then we adjust for the league passing environment, by using this formula:

[Result in Step 2] * by (214.54/Avg_Team_Receiving_Yards_Per_Game).

Why 214.54? Because that’s how many yards the average NFL team has passed for in each season since 1970.

4) Finally, we need to adjust for schedule length. This one’s pretty simple:

[Result in Step 2] * 16 / Team Games

As it turns out, the single-season leader in True Receiving Yards is….. Harold Jackson for the 1973 Rams. That will probably surprise some folks; heck, it surprised me. So let’s walk through Jackson’s season by comparing it to Calvin Johnson’s 2012. Jackson caught 40 passes for 874 yards and 13 touchdowns. That gives him 1,334 Adjusted Catch Yards, while Megatron’s 122-1964-5 translates to 2,674 Adjusted Catch Yards, more than twice what Jackson produced.

1) First, we need to convert those ACY numbers into receiving yards. In 1973, that conversion ratio is 65.5%, and in 2012, it was 64.5%; this means Jackson is credited with 874 receiving yards (ironically, his actual number) while Johnson is pushed down to only 1,725 yards. This is because Johnson had a ton of yards but only five touchdowns. In other words, based on his receptions, receiving yards, and receiving touchdowns, Johnson was more like a 1,725-yard receiver last year.

2) Jackson’s Rams had just 288 Team Pass Attempts, while the average team in 1973 averaged 373.3 pass attempts. So we need to bump Jackson up by 29.6%, which would give him 1,132 receiving yards. The 2012 Lions had 769 Team Pass Attempts compared to a league average of 592.4; therefore, we need to give Johnson credit for only 77% of his ACY, bringing him down to 1,329 receiving yards.

3) Next, we adjust for league environment. In 1973, the average team passed for 159 yards per game, which means we need to bump Jackson up by 34.6% (the result of 214.54 divided by 159); this gives him 1,524 receiving yards. For Megatron, since the average team in 2012 passed for 246 yards per game, we need to multiply his result in step 2 by 87.2%, leaving him with only 1,159 receiving yards.

4) For Calvin Johnson, that’s it: he is credited with 1,159 True Receiving Yards, after reducing his numbers for playing in a pass-happy offense, playing in a pass-happy era, and not having many touchdowns. For Jackson, his 1,524 gets pro-rated to a 16-game season, giving him 1,742 True Receiving Yards.
The table below shows the number of True Receiving Yards for the top 200 receivers since 1970. Let’s walk through Paul Warfield’s 1971 season, #4 on the list, as an example. That year, his 43-996-11 stat line translates to 1,431 Adjusted Catch Yards. The Adjusted Receiving Yards to Receiving Yards ratio for the entire league that season was 66.6%, so that translates to 953 receiving yards for Warfield. We multiply that number by the average number of pass attempts in the league that year (392) and divide it by the number of pass attempts by Miami (318) to get 1,174 yards. Next, we multiply that by 214.54 (the average receiving yards per game over the 43-year period) and divide by 174, which represents the low-octane era of 1971; that gives us 1,449 yards. Finally, we pro-rate to 16 games, and end up with 1,656 True Receiving Yards.

The trouble with directly using 1st downs, of course, is that we wouldn’t have that data for but a fraction of the historical seasons we’re trying to look at here (and this dataset only goes back to the merger). But no doubt somebody like Bobby Engram — long a Football Outsiders darling b/c of his remarkable ability to get 1st downs — is getting underrated here because we’re not measuring 1st downs directly. Engram never had more than 942 True Rec Yds in a season, and only cracked 800 3 times, but probably would be a lot higher if we factored in actual 1st downs instead of using catches as a proxy.

Kibbles

In addition to Engram, using a flat proxy would also be expected to hurt deep threats like Warfield. For instance, Vincent Jackson (17.8 career ypr) has gotten a first down on 84% of his receptions. Calvin (16.1 ypr) is at 76%. Steve Smith (14.7 ypr) has converted 63% of his catches into a new set of downs. Percy Harvin (11.8 ypr) has done it just 59% of the time. Welker (11.2 ypr) is at 57%. Danny Amendola and his paltry 8.9 ypr has converted just 49% of receptions into a first down. I’d imagine there’s a relatively linear relationship between average yards per receptions and average first downs per reception, and the flat proxy could be replaced by a scaled one.

Of course, that’s easy for me to say, since I wouldn’t be the guy calculating the relationship or updating the formulas…

ryan

Great work neil and chase…will yoou be posting a career list tomorrow or sometime later?

Also, here’s my pre-emptive disclaimer: I don’t think this is in any way the be-all or end-all of receiving stats, and I realize it’s controversial to have a season like Calvin Johnson’s rank 183rd since 1970. The league passing attempts/team passing attempts adjustment will be a particularly upsetting factor to some readers. However, this metric is a simple way to codify all of the adjustments we can currently make to a receiver’s basic boxscore stats.

Think about it: we’ve adjusted raw yardage for pretty much everything we can — catches (a proxy for 1st downs), TDs, schedule length, league passing environment, and yes, even the general number of opportunities a receiver had to catch the ball relative to his peers. Perhaps the latter adjustment is too strong; I certainly can’t prove it isn’t. However, I also think it’s more important to make that adjustment in some way than to ignore it completely. Perhaps further research will help us know exactly how much we should take into account the differences in team passing attempts between 2 receivers, but for now I don’t think it’s that unreasonable of an assumption to say that Calvin Johnson had 60% more opportunities to rack up receiving stats than somebody like Michael Crabtree did in 2012.

Tom Gower

I’m pretty skeptical there’s the sort of strictly linear relationship between team passing attempts and receiver catches the methodology seems to assume, especially when I see 25 of the top 30 receivers played for below-average passing volume teams, 14 of them for teams that passed at least 10% less than the average team.

Chase Stuart

Thanks, Tom. Neil and I have are doubts on that, too, but we’re trying to look into that.

One thing to keep in mind: in general, good teams pass less (especially for most of the 43-year period in question). So to the extent the best wide receivers are on the best teams, we would expect them to play for below-average pass volume teams. The ’73 Rams were 1st in socring, 1st in points differential, and 4th in points allowed. As a result, they ended up leading the league in rushing attempts. They had a very good running game, too.

Chase Stuart

I’ll also note the following. I’m quite confident that to the extent this system is friendly to low-pass volume teams, the magnitude of the bias is significantly smaller than the extent normal metrics are biased towards high-pass volume teams.

Tom Gower

Yeah, conceptually I have no problem with some sort of adjustment for volume-related adjustment.

To the extent pass attempts are a function of game situation, I’d want to attempt to isolate receivers from defense. That the Rams ranked fourth in points allowed is more or less orthogonal to how good Jackson was, in my point of view. It’s a tricky adjustment to make, especially if you want to conceptually tease out the concepts of best receiving seasons and passing seasons most dependent on a single receiver. The list works well for the latter; I’m much less convinced it does for the former.

Bowl Game Anomaly

I don’t necessarily think the system should be friendly to low-pass volume teams at all. While the WRs on high-pass volume teams got a lot more opportunities, they were also a much more critical part of their teams’ offenses. I’ve seen people argue that we shouldn’t downgrade RBs from the 70’s for having low YPC and looking to modern eyes like compilers because the offensive style at the time was run-heavy, but you can’t have it both ways. If RBs were more important in the 70’s than now, then WR’s were less important. I guess what I’m arguing is that if you replaced Harold Jackson, Cliff Branch, or Paul Warfield with JAG, their teams wouldn’t suffer all that much compared to how the Lions would suffer if Calvin Johnson was replaced with with JAG.

Chase Stuart

From a value standpoint, I might be inclined to agree with you. The ’74 Raiders led the NFL in points and points differential; unfortunately, they ranked only 23rd in attempts out of 26 teams (but 1st in Net Yards per Attempt).

Is the argument that if Branch was better, Oakland would have passed more? I find that hard to believe. How do you compare Branch’s 60-1092-13 on a team with 359 pass attempts to Calvin Johnson’s season on a Lions teams with 769 passes? Do you think Johnson’s season was better?

Bowl Game Anomaly

No, I’m not arguing that the Raiders would have passed more, but I don’t know what “better” means. Who was more valuable? Johnson. Who contributed more relative to the opportunities he was given? Probably Branch. So if you’re measuring actual contribution, then the adjustment makes no sense, but if you’re trying to measure talent in a vacuum, I can see why you would make the adjustment. So as long as we’re clear that the purpose of True Receiving Yards is estimate how good guys like Jackson and Branch might look if they got the chance to play in more favorable circumstances, and not an estimate of how valuable their contributions actually were, then I’m OK with it.

Basically I’m saying that this is a list of the best hypothetical WR seasons, not a list of the best actual WR seasons.

That’s the right idea. It’s not trying to measure actual value, because like you said, receivers from the 1970s were literally less valuable than they would have been in any other era due to the run-oriented nature of the game. So on the spectrum laid out by this post, True Receiving Yards would fall on the “ability” end.

Now, in light of Dave’s comments, I’m definitely going to refine the team passing attempts adjustment, but the basic goal of even the version above was to project what a receiver “would have” produced in a neutral league.

I think the version of the data Chase was working off didn’t have TEs included, but we can easily compute it for WRs, TEs, RBs, you name it.

Dave

For one I think it’s best not to even try to compare across eras even thought we often try. Also we have at least what 20 + years of WR target data right? Well maybe not that much in the pfr database. It seems like a waste to not use that. I’d rather see a pre-target list and post.

In we reality we know that Calvin Johnson had 203 targets to 150 for Steve Smith or a 35% difference. If we just use team passing attempts then we get 727/449 or the formula says that he had 62% more opportunities. Granted he had more plays on which to be a target but even the best WR isn’t going to be the main target on every pass play.So we might be skewing things in the opposite direction towards low volume passing teams. Let’s quickly dig a little deeper

So I did a quick and not very rigorous data collection and analysis but it will help illustrate my point. I pulled WR data from advancednflstats.com from 2005,2009,2012 regular season stats only.My X data column was team pass plays for those WR. Pass Attempts= passes+Sacks. My Y Collumn was targets per game played with a minimum of 12 games played.

The first data set had n=211 with team pass plays ranging from 769 to 411 and WR targets per game ranging from 3.4 to 13.2

So running a regression on the data set. You get and r-squared of 0.1 which means there is only a very loose correlation between the number of team passing attempts vs the number of targets a WR gets a game. Each additional passing attempt was on average worth 0.16 extra targets or an additional 16% of the team targets.

Then I restricted the data set further to guys getting a fair amount of targets I set the cutoff at 100 targets or 6.3 per game. This cut my data set down to an N of 120. Our min and max team passing attempts are still the same. But now our r-sqaured was down to 0.04. Very weak. And now each additional team passing attempt was on average only worth an additional 0.07 targets PER SEASON per team pass with a constant of 91 targets PER SEASON.

Let’s pretend that number is what we should use. Taking the Steve Smith / Calvin Johnson case pretending we don’t know how many targets they got. Just using team pass attempts we think Calvin had 769/477 =61% more opportunities. Using the formula above (91+0.07*769)/(91+0.0.07*477) = 145/124 = only an EXPECTED 16% more opportunities (targets)

So I think this idea definitely needs some more refinement as far as how to adjust for team passing attempts.

Chase Stuart

Can you run those numbers but only using the top receivers on each team? Otherwise, I think it might jumble the results.

Dave

Okay I did the following. Only took WR’s with 16 games played. Only selected the top WR on the team. And removed any WR’s with less than 100 targets. This gave me an N of 50. So small sample size theatre which could be improved with using more seasons but I got an r-squared of 0.096 with the following trendline:

Using this same data set:
An average 100+target WR on a 450 pass attempt team can expect 28% of the team targets
An average 100+target WR on a 750 pass attempt team can expect 21% of the team targets

Theoretically his makes sense as a team that passes a lot on average has more good WR’s to throw to than one that throws very little. Or they have better QB that is better at spreading the ball around rather than force feeding one guy.

Ok, so I got a chance to look at this… I took all of the WRs in the dataset, who played in and started 16 games in back-to-back seasons (Y and Y+1). They had to be between age 23-30 in year Y. The sample was 245 pairs of player-seasons, after removing 2 extreme outliers: Drew Hill 1985 (went from 335 TRY w/o the team attempt adjustment in 16 gs in 1984 to 1048 in 1985), and our friend Roger Carr 1976 (went from 591 to 1438).

Anyway, the experiment was set up like this: for each player-season in the pair, I recorded how many True Receiving Yds they had *before* the team passing att adjustment (so only adjusting for schedule length and league passing environment). I also recorded their team’s ratio of dropbacks to the average team’s dropbacks. If there were a perfectly linear, 1-to-1 effect of team dropbacks on production (which we assumed in TRY v1.0), then I’d be able to predict the % change in TRY from year Y to Y+1 just by looking at the ratio of tm/lg dropbacks from Y to Y+1.

For instance, in 1979 Alfred Jenkins had 831 TRY before the team att adjustment, and his team’s ratio of dropbacks to the NFL avg was 1.063. In 1980, he started 16 games again for a team with a ratio of 0.954. That means we’d expect Jenkins’ production to decline by 10.3%, derived from (.954/1.063)-1. In reality, though, he improved it by 14% (948 TRY). So that’s one data point.

Do that for all 245 pairs of seasons, and by no means does the regression have a high R^2 (it’s about 0.03)… however, the coefficient on the expected difference, 0.403, is very significant. That basically means that if there’s a 30% increase in team dropbacks, we should predict a 12% increase (40% of the difference between zero and 30%) in productivity/opportunity. This is pretty consistent with what Dave found in his comments:

That means Hines Ward, for instance, should only be getting a 15.7% productivity boost in 2004 when PIT threw 39% less than the average team. And Calvin Johnson should only be dinged by 9.2% instead of 23%. Which, I think, is a lot more reasonable than the original version of the formula.

Calvin Johnson 2012 still checks in 37th with 1,366 TRY, but that’s as much a function of the heavy environment adjustment (12.8% more receiving YPG in 2012 than the 1970-2012 avg) as anything else. He’s now 2nd only to Brandon Marshall among 2012 receivers.

Dave

Awesome! CJ at 37th seems much more reasonable.

Chase Stuart

I looked at all receivers since 1970 to play in at least 12 games and to have at least 400 receiving yards.

I then separated the receivers, by game, into their three highest attempt games and their three lowest attempt games.

In the HIGH attempt games, the teams passed 45.7 times, and the receivers recorded 91.7 ACY; they averaged 2.03 ACY/Attempt if you take an average of the average ACY/Att, and 2.01 ACY/Att if you divide 91.7 by 45.7. [Note: I think the latter is the more appropriate method, but I’m open to a counter argument.]

In the LOW attempt games, the teams passed 24.6 times, and the receivers recorded 63.6 ACY; they averaged 2.63 ACY/Attempt taking an average of the averages, and 2.58 if you divide 63.6 by 24.6.

So yes, in low-attempt games, WRs average more ACY/Attempt. On one hand, though, this is probably because WRs are doing a better job in high-attempt games than low-attempt games. Putting that issue aside, what does that mean?

When you increase pass attempts by 85.5%, you increase ACY by 44.3%; that implies a 52% ratio, not the 40% Neil got.

Chase Stuart

If you just take the highest attempt game and lowest attempt games, you get:

This implies that for a 128% increase in pass attempts, you only get a 63% increase in ACY, which implies a 50% ratio.

Chase Stuart

Since we seem to be using the comments as a think tank….

I just ran a regression using these inputs on WR games, with the minimums of 12 games and 400 receiving yards (and 1970):

Team Pass Attempt in Game X
Avg ACY/G in All Games that season but Game X
Avg TPA in all Games that season but Game X

My output was ACY in Game X

The best-fit formula was

9.7 + 1.364*TPA_G_X + 0.725*ACY/G_Avg – 1.05*TPA_Avg

Say a WR averages 100 ACY/G. If his team averages 40 attempts per game, and has 40 attempts in Game X, he’s projected at 94.7 ACY. If his team averages 40 att/g, and he has 50 attempts in Game X, he’s projected at 108.3 ACY. If his team instead throws 30 passes, he’s projected at 81.1 ACY. [One interpretation of this: If his team throws 66.67% more passes, he gains 33.5% more receiving yards.]

Now, say his team averages 30 attempts/game normally, but he’s still a 100 ACY/G guy. In a 30-attempt game, he’s projected at 91.6; in a 40-attempt game, 105; in a 50-attempt game, 118.9.

That “works” but I don’t know what we do with it. [One interpretation of this: If his team throws 66.67% more passes, he gains 29.8% more receiving yards.]

Dave

“That “works” but I don’t know what we do with it. [One interpretation of this: If his team throws 66.67% more passes, he gains 29.8% more receiving yards.]”

Going back to the Steve Smith/ Calvin Johnson example this very close to what actually happened. DET threw 61% more than CAR but CJ only gained 25% more receiving yards.

Dave

Just intuitively the main reason we can’t just divide by team passing attempts is realistically a top WR only gets targeted on about 25-30% of pass plays.

Tim Truemper

I think Tom Gower is on to something on the low passing volume bias (arithmetically). Not being a math whiz, still I can’t help to think about what I learned in the past about restricted ranges and how they affect data magnitude. I look at one specific case from the list above and how it shows a low volume output qualified with the relative passing volume adjustments,and as a result this one receiver’s actual performance makes the list:

1973 Paul Warfield 29 catches 514 yards 11 TD’s.

It is an amazing ratio of TD’s to catches but the absolute #’s are so low. It strikes me that the denominators used against the derived numerators would give a bias toward a higher derived adjusted receiving yards. If I get the time I may compute some other eras and see how they come out. i.e. 1950’s or 1960’s since the data from PFR should be available. I like the described derivation of Neil’s for WR performance as it stimulates discussion and provides a new way to consider player performance across areas and also with the within groups consideration of strength of schedule.

Dave

Sorry my 2nd point didn’t make sense but this one will. There are also a strong trend between the percent of the team pass plays the WR will get targeted vs how many pass plays the team runs. My cuttoff for this was 100 prorated targets

The R-squared on this regression was about 0.2

The average 100+ target WR on a 450 pass attempt team will average 27% of the teams targets
The average 100+ target WR on a 750 pass atempt team will average 18% of the teams targets

I took the same sample of players I used for my year-to-year study, and I re-ran the same experiment as before, except I used in-season splits instead of back-to-back seasons. Specifically, I used the ratio of team dropbacks in odd-numbered games to dropbacks in even-numbered games to try to predict the change in ACY from even to odd-numbered games.

The regression once again had a very low R^2 but a significant coefficient on expected change in ACY, and that coefficient was 0.779!

So it’s all over the place. I think Chase’s 50% number is probably the best bet, if not simply because it splits the difference between all of the different results we’ve seen, and it’s pretty convenient. I’d be willing to settle on that as the “official” discount rate on team dropbacks vs league dropbacks in the TRY formula.